Field theory on the q-deformed fuzzy sphere II:: quantization

[摘要] We study the second quantization of field theory on the q-deformed fuzzy sphere for q is an element of R. This is performed using a path integral over the modes, which generate a quasi-associative algebra. The resulting models have a manifest U-q (su(2)) symmetry with a smooth limit q --> 1, and satisfy positivity and twisted bosonic symmetry properties. A systematic way to calculate n-point correlators in perturbation theory is given. As examples, the 4-point correlator for a free scalar field theory and the planar contribution to the tadpole diagram in phi(4) theory are computed. The case of gauge fields is also discussed, as well as an operator formulation of scalar field theory in 2(q). + 1 dimensions. An alternative, essentially equivalent approach using associative techniques only is also presented. The proposed framework is not restricted to two dimensions. (C) 2002 Elsevier Science B.V. All rights reserved.

[发布日期] 2002-09-01

[关键词] fuzzy sphere;quantum group;quantization;non-commutative geometry